Bit width, sampling rate, compression, and even prediction are well illustrated by an extremely simple, interesting, and important technique called delta modulation or single-bit encoding. This algorithm is commonly used in commercial digital sound equipment.
We know that if we sample very fast, the change in the y-axis or amplitude of the signal is going to be extremely small. In fact, we can more or less assume that its going to be nearly continuous. This means that each successive sample will change by at most 1. Using this fact, we can simply store the signal as a list of 1s and 0s, where 1 means "the amplitude increased" and 0 means "the amplitude decreased." The good thing about delta modulation is that we can use only one bit for the representation: were not actually representing the signal, but rather a kind of map of its contour. We can, in fact, play it back in the same way. The disadvantage of this algorithm is that we need to sample at a much higher rate in order to ensure that were catching all the minute changes.
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